A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.

\(\text{(A)}\, SML \qquad \text{(B)}\, LMS \qquad \text{(C)}\, MSL \qquad \text{(D)}\, LSM \qquad \text{(E)}\, MLS\)

Select the most appropriate letter.

Guest Jan 23, 2019

#1**+1 **

Let the price of the small size = P and let the quantity contained = Q

So....the unit price is P /Q

Let the price of the meduim size = 1.5P

And let the quantity contained be (2 - ..20)Q = 1.8Q

So.....the unit price is (1.5)P / (1.8)Q = (5/6)P/Q

The large size price is (1.5)(1.3)P = 1.95 P

And the quantity is 2Q

So.....the unit price is (1/95 P) / ( 2Q) = (19/20)P/Q

So.....the best value from best to worst is

( 5/6)P/Q (19/20)P/Q P /Q =

M L S

CPhill Jan 23, 2019